{"title":"据difunctions","authors":"Roland Backhouse , José Nuno Oliveira","doi":"10.1016/j.jlamp.2023.100878","DOIUrl":null,"url":null,"abstract":"<div><p>The notion of a difunction was introduced by Jacques Riguet in 1948. Since then it has played a prominent role in database theory, type theory, program specification and process theory. The theory of difunctions is, however, less known in computing than it perhaps should be. The main purpose of the current paper is to give an account of difunction theory in relation algebra, with the aim of making the topic more mainstream.</p><p>As is common with many important concepts, there are several different but equivalent characterisations of difunctionality, each with its own strength and practical significance. This paper compares different proofs of the equivalence of the characterisations.</p><p>A well-known property is that a difunction is a set of completely disjoint rectangles. This property suggests the introduction of the (general) notion of the “core” of a relation; we use this notion to give a novel and, we believe, illuminating characterisation of difunctionality as a bijection between the classes of certain partial equivalence relations.</p></div>","PeriodicalId":48797,"journal":{"name":"Journal of Logical and Algebraic Methods in Programming","volume":"134 ","pages":"Article 100878"},"PeriodicalIF":0.7000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On difunctions\",\"authors\":\"Roland Backhouse , José Nuno Oliveira\",\"doi\":\"10.1016/j.jlamp.2023.100878\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The notion of a difunction was introduced by Jacques Riguet in 1948. Since then it has played a prominent role in database theory, type theory, program specification and process theory. The theory of difunctions is, however, less known in computing than it perhaps should be. The main purpose of the current paper is to give an account of difunction theory in relation algebra, with the aim of making the topic more mainstream.</p><p>As is common with many important concepts, there are several different but equivalent characterisations of difunctionality, each with its own strength and practical significance. This paper compares different proofs of the equivalence of the characterisations.</p><p>A well-known property is that a difunction is a set of completely disjoint rectangles. This property suggests the introduction of the (general) notion of the “core” of a relation; we use this notion to give a novel and, we believe, illuminating characterisation of difunctionality as a bijection between the classes of certain partial equivalence relations.</p></div>\",\"PeriodicalId\":48797,\"journal\":{\"name\":\"Journal of Logical and Algebraic Methods in Programming\",\"volume\":\"134 \",\"pages\":\"Article 100878\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Logical and Algebraic Methods in Programming\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2352220823000329\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Logical and Algebraic Methods in Programming","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2352220823000329","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
The notion of a difunction was introduced by Jacques Riguet in 1948. Since then it has played a prominent role in database theory, type theory, program specification and process theory. The theory of difunctions is, however, less known in computing than it perhaps should be. The main purpose of the current paper is to give an account of difunction theory in relation algebra, with the aim of making the topic more mainstream.
As is common with many important concepts, there are several different but equivalent characterisations of difunctionality, each with its own strength and practical significance. This paper compares different proofs of the equivalence of the characterisations.
A well-known property is that a difunction is a set of completely disjoint rectangles. This property suggests the introduction of the (general) notion of the “core” of a relation; we use this notion to give a novel and, we believe, illuminating characterisation of difunctionality as a bijection between the classes of certain partial equivalence relations.
期刊介绍：
The Journal of Logical and Algebraic Methods in Programming is an international journal whose aim is to publish high quality, original research papers, survey and review articles, tutorial expositions, and historical studies in the areas of logical and algebraic methods and techniques for guaranteeing correctness and performability of programs and in general of computing systems. All aspects will be covered, especially theory and foundations, implementation issues, and applications involving novel ideas.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
